Finite element matrices in congruent subdomains and their effective use for large-scale computations

Suzuki, Atsushi; Tabata, Masaaki

doi:10.1002/nme.1248

Cited by 3 publications

(4 citation statements)

References 21 publications

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“…We have performed numerical experiments and found that the plume number increases from 4 to 12 when the viscosity ratio increases from 10 3 to 10 4 under some condition. The detail of the numerical results will be presented in a forthcoming paper [9,10].…”

Section: Discussionmentioning

confidence: 99%

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Finite element approximation to infinite Prandtl number Boussinesq equations with temperature-dependent coefficients—Thermal convection problems in a spherical shell

Tabata

2006

Future Generation Computer Systems

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Section: Discussionmentioning

confidence: 99%

“…We can show that those equations are uniquely solvable. Once θ n h is given, (u n h , p n h ) is obtained from (9) and (10). Substituting θ n h and u n h to (11), θ n+1 h is solved.…”

Section: Remarkmentioning

confidence: 99%

Finite element approximation to infinite Prandtl number Boussinesq equations with temperature-dependent coefficients—Thermal convection problems in a spherical shell

Tabata

2006

Future Generation Computer Systems

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“…Tabarraei and Sukumar [11] demonstrated that, for the special case of quadtree meshes, for the Poisson equation and for the elasticity problem, the stiffness matrix of a subelement is the same as the stiffness matrix of the parent. Suzuki and Tabata [20] also showed the importance of reusing previous calculations studying the structure of the finite element mass and stiffness matrices of congruent subdomains (each of them being an image of a reference subdomain by an affine transformation, see [20] for further details). As a result, Suzuki and Tabata were able to express the global matrices as functions of the submatrices in the reference subdomain.…”

Section: Hierarchical Properties Between Geometrically Similar Elementsmentioning

confidence: 99%

A hierarchical h adaptivity methodology based on element subdivision

Ródenas

Albelda

Tur

et al. 2017

revuin

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Este artículo puede compartirse bajo la licencia CC BY-ND 4.0 y se referencia usando el siguiente formato: J.J. Ródenas, J.Albelda, M. Tur, F.J. Fuenmayor, "A hierarchical h adaptivity methodology based on element subdivision", UIS Ingenierías, vol. 16, no. ABSTRACTThis paper presents a hierarchical h adaptive methodology for Finite Element Analysis based on the hierarchical relations between parent and child elements that come out if these elements are geometrically similar. Under this similarity condition the terms involved in the evaluation of element stiffness matrices of parent and child elements are related by a constant which is a function of the element sizes ratio (scaling factor). These relations have been the basis for the development of a hierarchical h adaptivity methodology based on element subdivision and the use of multipoint-constraints to ensure C 0 continuity. The use of a hierarchical data structure significantly reduces the amount of calculations required for the mesh refinement, the evaluation of the global stiffness matrix, element stresses and element error estimation. The data structure also produces a natural reordering of the global stiffness matrix that improves the behaviour of the Cholesky factorization. KEYWORDS:Adaptive Modelling, Hierarchical properties, Mesh Enrichment, Mesh Generation. RESUMENEn este artículo se presenta una metodología h adaptativa para el Análisis por Elementos Finitos basada en las relaciones jerárquicas entre elementos padre e hijo que surgen si estos elementos son geométricamente similares. Bajo esta condición de similitud, los términos resultantes de la evaluación de las matrices de rigidez de elementos padre e hijo están relacionados por una constante que es una función de la relación de tamaños de elemento (factor de escala). Estas relaciones han sido la base para el desarrollo de una metodología jerárquica h adaptativa basada en la subdivisión de elementos y el uso de restricciones multipunto para asegurar la continuidad C 0 . El uso de una estructura de datos jerárquica reduce significativamente la cantidad de cálculos requeridos para el refinamiento de la malla, la evaluación de la matriz de rigidez global, las tensiones de los elementos y la estimación del error del elemento. La estructura de datos también produce un reordenamiento natural de la matriz de rigidez global que mejora el comportamiento de la factorización de Cholesky. PALABRAS CLAVE:Modelado Adaptativo, Propiedades jerárquicas, Enriquecimiento de malla, Mallado.

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“…elstct1 was used in [18]. Matrices stokes1 and stokes2 are obtained from a P 1-P 1 stabilized finite element discretization of the Stokes equations in a three-dimensional domain [36]. The matrix stokes1 is set with stress free boundary conditions, and then it has the six dimensional kernel corresponding to all rigid body modes of velocity and stokes2 with Dirichlet boundary conditions, the one dimensional kernel to a pressure lifting.…”

Section: Advantage Of Task Scheduling With Asynchronous Executionmentioning

confidence: 99%

A dissection solver with kernel detection for symmetric finite element matrices on shared memory computers

Suzuki

Roux

2014

Numerical Meth Engineering

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SUMMARYA direct solver for symmetric sparse matrices from finite element problems is presented. The solver is supposed to work as a local solver of domain decomposition methods for hybrid parallelization on cluster systems of multi‐core CPUs, and then it is required to run on shared memory computers and to have an ability of kernel detection. Symmetric pivoting with a given threshold factorizes a matrix with a decomposition introduced by a nested bisection and selects suspicious null pivots from the threshold. The Schur complement constructed from the suspicious null pivots is examined by a factorization with 1 × 1 and 2 × 2 pivoting and by a robust kernel detection algorithm based on measurement of residuals with orthogonal projections onto supposed image spaces. A static data structure from the nested bisection and a block sub‐structure for Schur complements at all bisection levels can use level 3 BLAS routines efficiently. Asynchronous task execution for each block can reduce idle time of processors drastically, and as a result, the solver has high parallel efficiency. Competitive performance of the developed solver to Intel Pardiso on shared memory computers is shown by numerical experiments. Copyright © 2014 John Wiley & Sons, Ltd.

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Finite element matrices in congruent subdomains and their effective use for large-scale computations

Cited by 3 publications

References 21 publications

Finite element approximation to infinite Prandtl number Boussinesq equations with temperature-dependent coefficients—Thermal convection problems in a spherical shell

Finite element approximation to infinite Prandtl number Boussinesq equations with temperature-dependent coefficients—Thermal convection problems in a spherical shell

A hierarchical h adaptivity methodology based on element subdivision

A dissection solver with kernel detection for symmetric finite element matrices on shared memory computers

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